Problem: Integrate. $ \int 16\cos(x)\,dx $ $=$ $+ C$
We need a function whose derivative is $16\cos(x)$. We know that the derivative of $\sin(x)$ is $\cos(x)$, so let's start there: $\dfrac{d}{dx} \sin(x) = \cos(x)$ Now let's multiply by $16$ : $\dfrac{d}{dx}\left[ 16\sin(x) \right]= 16\cos(x)$ Because finding the integral is the opposite of taking the derivative, this means that: $ \int 16\cos(x)\,dx =16 \sin(x)\, + C$ The answer: $16\sin(x)+C$.